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The power electronic converters and grid‐connected filters were important components of the permanent magnet direct drive wind power generation system whose performance directly determines the quality of wind power generation. In past modeling, analysis, and control studies, capacitive and inductive components were often treated as integral‐order components. However, the inductance and capacitance components in the actual permanent magnet direct drive wind generator were fractional‐order components, and their electrical characteristics will change with the change of order, which had an important impact on the dynamic and static characteristics of the system. In this paper, the mathematical model of the fractional‐order LCL (FOLCL) filter was derived. Through simulation, it could be seen that the FOLCL filter can avoid resonance fundamentally. At the same time, the fractional‐order PI (FOPI) controller was introduced into the machine‐side current converter, and the parameters of the FOPI controller of the outer speed loop and the inner current loop were adjusted by using the time‐domain optimization method. The results showed that the efficiency of the FOPI controller was significantly better than that of the integer‐order PI controller in realizing maximum wind energy capture. It provides theoretical support and practical application value for the stable operation of the wind power generation system.

The article proposes a model in which Diffusion Approximation is used to analyse the TCP/AQM transmission mechanism in a multinode computer network. In order to prevent traffic congestion, routers implement AQM (Active Queue Management) algorithms. We investigate the influence of using RED-based AQM mechanisms and the fractional controller PIγ on the transport layer. Additionally, we examine the cases in which the TCP and the UDP flows occur and analyse their mutual influence. Both transport protocols used are independent and work simultaneously. We compare our solution with the Fluid Flow approximation, demonstrating the advantages of Diffusion Approximation.

Wastewater treatment plants (WWTPs) are highly non-linear processes that must be optimized to meet rigorous environmental water regulations. In this context, efficiency and costs are equally important terms. The ASM3bioP framework is employed in this study to enable simultaneous nitrogen and phosphorus removal using an activated sludge process model with seven-reactor configurations. The activated sludge process is the most complicated and energy-intensive phase of a WWTP. To control dissolved oxygen in aerobic reactors and nitrate levels in anoxic reactors, two robust PI controllers — a classical PI and a non-integer (fractional)-order PI — with both integer-order and fractional-order models are designed. The controllers are created and simulated with the use of a mathematical model that has been developed based on the input data. The lower level fractional controller with a fractional-order model improves both the effluent quality (EQI) and operational cost (OCI) indices significantly. For such biological WWTP, a hierarchical fuzzy logic controller is designed to adjust the dissolved oxygen in the seventh reactor (DO 7 ) to control ammonia. The implemented supervisory layer control strategy improves effluent quality EQI while increasing OCI marginally.

This chapter contains sections titled: Fractional Calculus Fractional Order Controls Fractional Order Motion Controls Contributions Organization